Spaniard Silvia Soler-Espinosa erased the Romanian Dulgheru 6-3, 6-3 on the hardcourts at Sierra Madre Tennis Club.
Sixth-seeded Hungarian Greta Arn avoided an upset by handling Chinese Zhang Shuai 6-1, 6-4.
Other Day-2 wins came for France's Alize Cornet, Croatian qualifier Maria Abramovic and Russian Valeria Savinykh, who drilled 41-year-old Japanese Kimiko Date-Krumm 6-2, 6-3. Abramovic topped last week's Bogota runner-up Alexandra Panova, 7-5, 6-4.
This week's champion will claim $37,000.